Here's a page of patterns for illustrating/learning some creative possibilities with a basic rock beat, using some simple displacements— playing one or more notes “late”, moving them over to the &:
Learn the patterns individually, then practice the entire page without stopping, playing the basic groove one time, alternating with each numbered groove played one or three times. Or you could do two measures of basic groove, two measures numbered pattern. Where there's no bass drum on the 1, it may help beginners to say “1” out loud. As soon as you're ready, it will be more fun (and educational) to run these with one of my practice loops.
Get the pdf